Differential speed reduction apparatus and double-toothed gear for use therein

ABSTRACT

The production of differential speed reduction apparatus, which uses a double-toothed gear including face cams having tooth profiles uniquely generated to secure efficient speed reduction. The speed reduction apparatus includes an input shaft carrying the double-toothed gear, a slant shaft wobbling in association with the rotation of the input shaft, a stationary face gear engageable with the face cams, a movable face gear secured to an output shaft, wherein the stationary face gear and the movable face gear have a roller-like or a convex-face contour.

BACKGROUND OF THE INVENTION

The present invention relates to a differential speed reductionapparatus and double-toothed gear for use therein and, moreparticularly, to a differential speed reduction apparatus employing adouble-toothed gear having a uniquely generated tooth profile.

It is known in the art to employ a double-toothed gear in thedifferential speed reduction apparatus, wherein the gear wobbles inassociation with the rotation of an input shaft. For example, JapanesePatent Publication (unexamined) No. 54-120347 discloses a typicalexample of the differential speed reduction apparatus of such kind.

This prior art apparatus comprises a double-toothed gear capable ofwobbling in association with the rotation of the input shaft, astationary gear, and a movable gear connected to the output shaft. Thesegears are engaged with each other in a unique manner, but the uniqueengagement requires a specially generated tooth profiles. As a matter offact, it is not easy to generate such unique gear profiles as to berequired by the prior art. This is the reason why the prior artapparatus has not been put into practice.

OBJECTS AND SUMMARY OF THE INVENTION

The present invention is directed toward solving the difficulty involvedin the conventional system for generating tooth profiles used indifferential speed reduction apparatus discussed above. Thus an objectof the present invention is to provide a differential speed reductionapparatus including a double-toothed gear having a profile adapted foruse in the differential speed reduction apparatus.

According to one aspect of the present invention, there is provided adifferential speed reduction apparatus, which comprising adouble-toothed gear including face cams at opposite sides, each face camhaving a tooth profile generated so as to be adapted for use in thedifferential speed reduction apparatus, which includes an input shaftcarrying the double-toothed gear, a slant shaft rotatively connected tothe input shaft such that the slant shaft wobbles in association withthe rotation of the input shaft, a stationary face gear engageable withthe face cams of the double-toothed gear, a movable face gear secured toan output shaft, wherein the stationary face gear and the movable facegear have a roller-like or a convex-face contour, and wherein the facecams of the double-toothed gear have a profile which satisfies thefollowing equation:

    B=tan.sup.-1 (cos θ·tan α),

    C=tan.sup.-1 (sin θ·tan α), and

    ΔA=D·θ/N.

where

α=1 the angle at which the slant shaft is inclined to the axis A--A' ofthe input shaft;

B°, C°=the angles of the face cams obtainable from α and θ at which theinput shaft rotates about the A--A';

ΔA°=D·θ/N;

D=a gear ratio in the mating face cam and face gear; and

N: the numbers of teeth of each face cam.

According to another aspect of the present invention, there is provideda system for generating a tooth profile adapted for use in adifferential speed reduction apparatus, the system comprising a B-axisNC rotary table reversibly the system comprising a B-axis NC rotarytable reversibly rotative about an axis B by an angle α, a C-axis NCrotary table provided on the B-axis rotary table, the C-axis table beingreversibly rotative about an axis C by an angle α, the axis Cintersecting with the axis B at right angle, an A-axis NC rotary tableprovided on the C-axis rotary table, the A-axis rotary table beingreversibly rotative about an axis A intersecting with the axis C atright angle, the A-axis rotary table including a rotary shaft, a gearblank holder secured to the rotary shaft, an end mill secured to thegear blank holder to cut the sides of a gear blank held by the gearblank holder, the end mill having a diameter equal to that of each facegear of a stationary gear and a movable gear, the A-axis rotary tablebeing driven to enable the gear blank to rotate by ΔA° at which a slantshaft wobbles, and the B-axis rotary shaft and the C-axis rotary shaftbeing driven to enable the blank to reversibly rotate by angles B° andC°, thereby generating a desired tooth profile.

Other objects and advantages of the present invention will become moreapparent from the following detailed description, when taken inconjunction with the accompanying drawings which show, for the purposeof illustration only, one embodiment in accordance embodiment inaccordance with the present invention.

The double-toothed gear having uniquely generated profiles at oppositesides takes the form of a cam having a roller-like or convex contour. Inthis specification these portions are called face cams so as todistinguish them from ordinary types of face gears.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic view exemplifying the underlying principle ofthe differential speed reduction apparatus using a double-toothed gearincluding tooth profiles generated according to the present invention;

FIGS. 2, 3a, 3b, 4 and 5 are diagrammatic views exemplifying a processfor generating the tooth profiles in accordance with the presentinvention;

FIG. 6 is a view showing the development of the tooth profile;

FIGS. 7a, 8a, 9a, 10a, 11a, are plan views illustrating a series ofsteps at which the tooth profile is progressively generated;

FIGS. 7b, 8b, 9b, 10b, 11b, are front views illustrating a series ofsteps at which the tooth profile is progressively generated;

FIG. 12 is a vertical cross-section through face cams having the toothprofiles generated according to the present invention;

FIG. 13 is a view showing a development of the face cam of FIG. 12; and

FIG. 14 is a cross-sectional view showing a main part of a differentialspeed reduction apparatus using the double-toothed gear.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIGS. 1 6, 7a, and 7b, the manner of generating the toothprofiles of face cams 11, 12 will be described:

FIG. 1 diagrammatically shows the underlying principle of a differentialspeed reduction apparatus employing the face cams 11, 12 whose profilesare generated according to the present invention. A double-toothed gear10 having the face cams 11, 12 on opposite sides is rotatively carriedon a slant shaft 2 connected to an input shaft 1 through a bearing 3.The input shaft 1 is carried on bearings 4, 5 such that it rotates aboutan axis A--A'.

A stationary face gear 13 and a movable face gear 14 each face thedouble-toothed gear 10. The stationary face gear 13 and the movable facegear 14 include rollers 15 and 16 engageable with the face cams 11 and12, respectively, which rollers 15 are radially arranged about the axisA--A'. Instead of the rollers 15 and 16 convex-face contour teeth can beused. The stationary gear 13 is fixed to a casing 6, and the movablegear 14 is connected to an output shaft 7 such that it rotates relativeto the casing 6. The output shaft 7 is concentric with the input shaft1, and carried on a bearing 8.

The speed reduction apparatus is operated as follows:

When the input shaft 1 is rotated, the double-toothed gear 10 revolveswith respect to the stationary face gear 13 and the movable face gear 14in accordance with the wobbling motion of the slant shaft 3.Simultaneously it rotates about its own center by an amount dependingupon the gear ratio between the rollers 15 and the face cam 11. However,since the face cam 11 is restrained in motion by the stationary facegear 13, the movable face gear 14 rotates by an amount depending uponthe gear ratio between the rollers 16 and the face cam 12, plus or minusthe axial rotations of the double-toothed gear 10. In this way the speedof rotation of the output shaft 7 is reduced. Herein the (+) means acase where the rotating direction of the movable face gear 14 and thatof the axial rotation of the double-toothed gear 10 are the same, andthe (-) means a case where they are in opposition. The speed reductionratios are changeable depending upon the numbers of teeth of the facecams 11, 12, the number of the rollers 15 of the stationary face gear13, and the number of the rollers 16 of the movable face gear 14. Now,suppose that:

N₁ =the number of rollers 15;

N₂ =the number of teeth of the face cam 11;

N₃ =the number of teeth of the face cam; and

N₄ =the number of rollers.

Therefore, the speed reduction ratio (i) is calculated as follows:

The rotation of the double-toothed gear 10 effected by the revolution ofthe face cam 11 relative to the rollers 15 is expressed by the equation:

    i.sub.1 =1-N.sub.1 /N.sub.2.

The speed reduction ratio (i₂) between the face cam 12 and the rollers16 is expressed by:

    i.sub.2 =N.sub.3 /N.sub.4.

The rotation of the rollers 16 effected by the revolution of the facecam 12 relative to the rollers 15 is expressed by the equation:

    i.sub.3 =1-N.sub.3 /N.sub.4.

The total speed reduction ratio (i) is obtained from the followingequation: ##EQU1## where: N₁ =19;

N₂ =18;

N₃ =19; and

N₄ =20 ##EQU2## when: N₁ =18;

N₂ =19;

N₃ =19; and

N₄ =20. ##EQU3##

As is evident from the comparison between the two results, a slightchange in gear ratios leads to a wide variation of speed reductionratios. The (+) means that the input shaft 1 and the output shaft 7rotate in the same direction, and the (-) means that they rotate in theopposite directions.

The manner of generating the tooth profiles of the face cams 11, 12 willbe described:

In accordance with the regular rotation of the input shaft 1 the facecams 11, 12 are also rotated by equal angles under certain conditions.Since the face cams 11, 12 are arranged in a plane perpendicular to theslant shaft 2, the angular displacement of the slant shaft 2 becomes animportant factor to consider for generating the tooth profile of the camfaces 11 and 12. Now, the slant shaft 2 and the input shaft 1 will beconsidered by reference to FIG. 2.

The slant shaft 2 is inclined at an angle of α° relative to the axisA--A' of the input shaft 1, and rotates about it by equal angles.Suppose that there is a point (P) spaced by a distance ι from the center0 of the slant shaft 2 where it intersects with the axis A--A' and thatthe point (P) rotates by an angle of θ° in a clockwise direction toshift to point (P'). The angles between the slant shaft 2 and the axisA--A' are B° and C°, are obtained in the following manner:

A horizontal component L of the distance ι on the axis A--A' isexpressed by the equation:

    L=ι·cos α.                             (1)

Suppose that a vertical component is Y and a horizontal component is X,each is expressed by the equation:

    R=L·tan α,                                  (2)

    X=R·cos θ, and                              (3)

    Y=R·sin θ.                                  (4)

    Therefore,

    tan B=Y/L, and

    tan C=X/L.

Substituting these for X and Y in (3) and (4) above results in thefollowing equation:

    B=tan.sup.-1 (R·cos θ/L) and                (5)

    C=tan.sup.-1 (R·sin θ/L).                   (6)

Substituting L=R/tan α of (2) for L,

B=tan⁻¹ (R·cos θ·tan α/R),

    ∴B=tan.sup.-1 (cos θ·tan α),  (7),

    C=tan.sup.-1 (R·sin θ·tan α/R),

    44 C=tan.sup.-1 (sin θ·tan α).        (8),

In this way the equations (7) an (8) are obtained. Herein, α is aconstant. Therefore, the angles B° and C° vary depending upon valuesderived from the equations (7) and (8) substituted by angulardisplacements θ.

Next, the angular displacement of the face cam 11 will be obtained:

The face cam 11 is angularly displaced in association with the inputshaft 1, and rotates about its own center by differences between thenumber of the rollers 15 (number of teeth) N₁ and the number of teeth N₂of the face cam 11. Let the difference in the number of teeth be D.Then, D=N₁ -N₂, wherein N₁ is a constant. Therefore, the rotations ofthe face cam 11 is D/N₂. This value can be derived in terms of angulardisplacement. Now, let an angular displacement of the face cam 11 be Afor one rotation of the input shaft 1, then:

    A=D·360°/N.sub.2.                          (9)

When the input shaft 1 rotates by θ°, then: ##EQU4##

Since D and N₂ are constants, it is understood that ΔA° varies inproportion to the angular displacement θ of the input shaft 1.

The values of ΔA°, angles B° and C° represent the angular displacementof the face cam 11 engageable with the rollers 15. It is derived fromthis that the equations (4) and (6) are formulas for generating thetooth profile.

The curves for generating the tooth profile in accordance with theseequations become three-dimensional, not planar. With reference to FIGS.3a, 3b, 4, 5, and 6, the development of the approximate tooth profile ofthe face cam 11 will be described:

In FIG. 6 it is presumed that the face cam 11 is stationary whereas therollers 15 rotate though the face cam 11 actually wobbles whilerotating.

In FIG. 3a, 3b, it is presumed that the face cam 11 is provided with acylindrical member 17 concentric with the slant shaft 2, the cylindricalmember 17 having a radius of K. Suppose that the cylindrical member 17moves over a distance ΔS when the face cam 11 rotates by ΔA°, then:

    ΔS/2πK=ΔA/2π, and

    ΔS=ΔA2·K.                             (11)

Substituting the equation (10) for ΔA in the equation (11) results inthe following:

    ΔS=D·θ·K/N.sub.2.            (12)

The angular displacement θ of the input shaft 1 is constant, whichconsists of one rotation divided by n. With the substitution of θ=2·π/nthe variations of tooth profile can be generated. Substituting thisvalue for the equation (12) results in the following relationship:

    ΔS=2·π·K·D/n·N.sub.2.(13)

If the tooth profile is to be recognized by unrolling the cylindricalmember 17, the decline of the face cam caused by an angular displacementof the axis C must be taken into consideration. FIG. 4 shows a statewhere the axis C is in the maximum angular displacement, and FIG. 5 isan enlarged view of the main portion of FIG. 4. Suppose that adisplacement of the roller from the axis of the face cam is DX. Then:

    DX=H·sin C°.                               (14)

If the matter is considered on the development view, the center of theroller is derived from by substituting the equation (14) for theequation (13), that resulting in:

    Xn=ΔS-DX.                                            (15)

A displacement in the direction of Y axis is approximately expressed interms of the angle B.

First, a distance y displaced in parallel with the axis A--A' in FIG. 3is determined, on the basis of which the 13 figure is drawn.

In FIGS. 3a, 3b suppose that a straight line C--C' passes through thecenter O of the slant shaft 2 and intersects with the axis A--A' atright angle, that the line C--C' is spaced from the axis of the rollers15 by a distance H, and that the axial center Q of the cylindricalmember 17 of the face cam 11 is displaced by h from the angle B. Then:

    h=K·sin α,

    y=H-h,

    Δh=K·sin B.

    Therefore,

    ΔY=H-Δh.                                       (16)

When the tooth profile is divided by n, Yn is expressed by the followingequation:

    Yn=H-K·sin {tan.sup.-1 (cos 2π/n)·tan α}.(17)

From the equations (15) and (17) n=20 and D=1 are respectively obtained,on the basis of which Xn and Yn are calculated. The values of Xn areplotted along a horizontal axis, and as shown in FIG. 6, circles havinga diameter equal to that of the roller 15 are drawn with the centers asthe intersections of Xn and Yn. In this way a desired tooth profile isapproximately obtained.

Referring to FIGS. 7a, 7b, 8a, 8b, 9a, 9b, 10a, 10b, 11a and 11b themanner of generating a tooth profile on the basis of angles ΔA°, B° andC° will be described by way of an example:

A B-axis NC rotary table 20 rotates about a vertical axis B by an angleα in a clockwise and counterclockwise direction, wherein the angle α isequal to the decline of angle of the slant shaft 2. A C-axis NC rotarytable 21 rotates about a horizontal axis C by an angle α in a clockwiseand counter clockwise direction, wherein the angle α is equal to thedecline of angle of the slant shaft 2. A third rotary or A-axis NCrotary table 22 has a rotary shaft 23 which rotates about an axis A(horizontal) intersecting with the axis C at right angle. The shaft 23includes a blank holder 24 whereby a blank 25 is maintained and a tailstock 26 is adapted to bear a free end of the rotary shaft 13.

An end mill 27 has the same diameter as that of the roller 15, and isdisposed at the same place as the roller 15 fixed in such a manner as tocut the sides of the blank 25. In FIGS. 7a, 7b, 11a, 11b , D is thecentral axis along which the NC operation is carried out, the centralaxis passing through the intersections of the axese A, B and C. Theworking is initiated from the intersections of these axese.

To initiate the operation: the B-axis NC rotary table 20 is rotateduntil it is angularly displaced by an angle α from the central axis D.At this stage the C-axis rotary table 21 takes a horizontal posture,under which the end mill 27 comes into engagement with the gear blank25.

Next, the A-axis NC rotary table 22 is driven to enable the blank 25 torotate intermittently by Δα. The B-axis NC rotary table 20 and theC-axis NC rotary table are rotated by the angle B and C, respectively.As shown in FIG. 9, when the B-axis NC rotary table 20 is displaced by αfrom the line D in the opposite direction, it is reversely rotated, andreturned to the original position shown in FIG. 7a, 7b by way of theposition shown in FIGS. 10a, 10b and 11a, 11b in the course of which thegear blank 25 is cut by the end mill 27 to have a tooth profile 18 onits side. Subsequently the same procedure is repeated until N₂ teeth isformed on the face cam 11. Then, the other side of the gear blank 25 iscut in the same manner until N₃ teeth are formed on the face cam 12. Inthis way a double-toothed gear 10 is finished as shown in FIG. 12. FIG.13 shows an unrolled phase (development) of the tooth profile of thedouble-toothed gear 10.

FIG. 14 shows a differential speed reduction apparatus using thedouble-toothed gear 10 produced in the above-mentioned manner, in whichthe principle illustrated in FIG. 1 underlies.

The input shaft 1 is provided with a slant shaft 2 in its middle portionwhich is inclined by an angle α. The slant shaft 2 carries thedouble-toothed gear 10 through bearings 3. The input shaft 1 is carriedon the casing 6 through bearings 4 and needle bearings 5 such that itrotates about the axis A--A'. The bearings 4 are accommodated in ahousing 30, which is threadally secured to a casing cover 6a at threads31 such that the bearings 4 are adjustable along the axis A--A' togetherwith the housing 30.

The output shaft 7 is concentric of the input shaft 1, and carried in asleeve 6b through bearings 8 and 9.

The double-toothed gear 10 is interposed between the stationary facegear 13 and the movable face gear 14, the latter being provided with N₁rollers 15 and N₄ rollers 16, respectively, which are radially arrangedon discs 13a and 14a with respect to the axis A--A'. The rollers 15 and16 are engageable with the face cams 11 and 12 of the double-toothedgear 10.

The disc 13a is secured to the casing 6 by an adjustable screw 32 and afixed screw 33 in such a manner as to be adjustable along the axisA--A'. The threads 31 of the housing 30, the adjustable screw 32 and thefixed screw 33 constitute a backlash compensating entity whereby therollers 15 are properly in mesh with the face cam 11.

The disc 14a is rotatively mounted on the inner end of the output shaft7.

The differential speed reduction ratio (i) of the apparatus is expressedby the equation:

    i=1-N.sub.1 ·N.sub.3 /N.sub.2 ·N.sub.4

As is evident from the foregoing description, the differential speedreduction apparatus according to the present invention has the a. Numberof advantages namely, a high reduction ratio; a low inertia, i.e., theinput shaft has a relatively small moment of inertia; a minimizedpossible backlash by adjustability of the face cams along the axisA--A'; and a minimum, if any, energy loss by virtue of the concentricarrangement of the input shaft and the output shaft. Moreover, the speedreducing efficiency is enhanced because of the rolling contact, and theface cams can withstand a high load, with one third of the teethtransmitting a torque enabling a large torque transmission.Additionally, the face cams are compact in size and lightweight becauseof the relatively small diameter, and the face cam can withstand a longperiod of use because they are not exposed to friction. Also, the entirestructure of the apparatus is simple and therefore easy to maintain, andthe rolling contact allows the cam faces to rotate high speeds.

What is claimed is:
 1. A differential speed reduction apparatus,comprising a double-toothed gear including face cams at opposite sides,each face cam having a tooth profile generated s as to be adapted foruse in the differential speed reduction apparatus including an inputshaft carrying the double-toothed gear, a slant shaft rotativelyconnected to the input shaft such that the slant shaft wobbles inassociated with the rotation of the input shaft, a stationary face gearengageable with the face cams of the double-toothed gear, a movable facegear secured to an output shaft, wherein the stationary face gearsecured to an output shaft, wherein the stationary face gear and themovable face gear have one of a roller-like or a convex-face contour,and wherein the face cams of the double-toothed gear have a profilewhich satisfies the following equations:

    B=tan.sup.-1 (cos Θ·tan α),

    C=tan.sup.-1 (sin Θ·tan α), and

    ΔA=D·Θ/N,

where: α=an angle at which the slant shaft is inclined with respect toan axis A--A' of the input shaft; θ=an angle at which the input shaftrotates about the axis A--A'; B°, C°=angles of the face cams obtainablefrom α and Θ; ΔA=D·Θ/N; D=a gear ratio in a mating face cam and facegear; and N=a number of teeth of each face cam.
 2. A double-toothed gearadapted for use in differential speed reduction apparatus, the gear, thedouble-toothed gear including face cams at opposite sides adapted torespectively engage a movable face gear and a stationary face gear eachhaving one of a roller-like or convex face contour, and wherein eachface cam has a tooth profile which satisfies the following equations:

    C=tan.sup.-1 (sin Θ·tan α), and

    C=tan.sup.-1 (sin Θ·tan α), and

    ΔA=D·θ/N,

where: α=an angle at which a slant shaft of the speed reductionapparatus is inclined with respect to an axis A--A' of an input shaft ofthe apparatus; θ=an angle at which the input shaft rotates about theaxis A--A'; B°, C°=angles of the face cams obtainable from α and Θ;ΔA°=D·Θ/N; D=a gear ratio in a mating face cam and face gear; and N=anumber of teeth of each face cam.